A new type of deformable model is presented that merges meshes and level sets into one representation to provide interoperability between methods designed for either. This includes the ability to circumvent the CFL time step restriction for methods that require large step sizes. The key idea is to couple a constellation of disconnected triangular surface elements (springls) with a level set that tracks the moving constellation. The target application for Spring Level Sets (SpringLS) is to implement comprehensive imaging pipelines that require a mixture of deformable model representations to achieve the best performance. We demonstrate how to implement key components of a comprehensive imaging pipeline with SpringLS, including image segmentation, registration, tracking, and atlasing.

A new data structure is presented for geometrically modeling multi-objects. The model can exhibit elastic and fluid-like behavior to enable interpretability between tasks that require both deformable registration and active contour segmentation. The data structure consists of a label mask, distance field, and springls (a constellation of disconnected triangles). The representation has sub-voxel precision, is parametric, re-meshes, tracks point correspondences, and guarantees no self-intersections, air-gaps, or overlaps between adjacent structures. In this work, we show how to apply existing registration algorithms and active contour segmentation to the data structure; and as a demonstration, the data structure is used to segment cortical and subcortical structures (74 total) in the human brain.

An emerging topic is to build image segmentation systems that can segment hundreds to thousands of objects (i.e. cell segmentation\tracking, full brain parcellation, full body segmentation, etc.). Multi-object Level Set Methods (MLSM) perform this task with the benefit of sub-pixel precision. However, current implementations of MLSM are not as computationally or memory efficient as their region growing and graph cut counterparts which lack sub-pixel precision. To address this performance gap, we present a novel parallel implementation of MLSM that leverages the sparse properties of the algorithm to minimize its memory footprint for multiple objects. The new method, Multi-Object Geodesic Active Contours (MOGAC), can represent N objects with just two functions: a label mask image and unsigned distance field. The time complexity of the algorithm is shown to be O((M (power)d)/P) for M (power)d pixels and P processing units in dimension d = {2,3}, independent of the number of objects. Results are presented for 2D and 3D image segmentation problems.

A novel algorithm is presented to segment and reconstruct injected bone cement from a sparse set of X-ray images acquired at arbitrary poses. The sparse X-ray multi-view active contour (SxMAC-pronounced "smack") can 1) reconstruct objects for which the background partially occludes the object in X-ray images, 2) use X-ray images acquired on a noncircular trajectory, and 3) incorporate prior computed tomography (CT) information. The algorithm's inputs are preprocessed X-ray images, their associated pose information, and prior CT, if available. The algorithm initiates automated reconstruction using visual hull computation from a sparse number of X-ray images. It then improves the accuracy of the reconstruction by optimizing a geodesic active contour. Experiments with mathematical phantoms demonstrate improvements over a conventional silhouette based approach, and a cadaver experiment demonstrates SxMAC's ability to reconstruct high contrast bone cement that has been injected into a femur and achieve sub-millimeter accuracy with four images.

This paper develops a sensor- and sampling-based motion planner to control a surgical robot in order to explore osteolytic lesions in orthopedic surgery. Because of the difficulty of using conventional surgical tools, such exploration is needed in minimally-invasive treatments of ¿particle diseases,¿ which commonly result from material wear in total hip replacements. Since a geometric model of the osteolytic cavity is not always available, the planner relies only on a robot model that can detect collisions. As such, the planner can work in conjunction with real systems. The planner effectively combines global and local exploration. The global layer determines which regions to explore, while local exploration uses information gain to move the robot tip to positions in the region that increase exploration. Simulation experiments are conducted using a snake-like cannula robot on surgically-relevant osteolytic cavities. As desired in minimally-invasive treatment of osteolysis, performance is measured as the volume explored by the robot tip. The proposed method achieves 83-92% performance rate when compared to methods that require 3D models of osteolytic cavities. Comparisons to sensor-based related work (i.e., no 3D models) show significant improvements in performance.